Question

If (3,3) (6,y) (x,7) or (5,6) are the vertices of a parallelogram taken in order,find the values of x and y​

Answer 1

★Given:-

• The points (3,3) (6,y) (x,7) or (5,6) are the vertices of a parallelogram taken in order.

★To find:-

• The values of x&y.

★Solution:-

Let ABCD is a parallelogram.

Then,

• A(3,3) , B(6,y) , C(,7) & D(5,6) are coordinates
• AC and BD are the diagonals.

Using the midpoint formula,

✦(x,y) = [(x₁+x₂) /2 ,(y₁+y₂)/2]

Where,

• (x,y) = coordinates of midpoint
• (x₁,y₁) = coordinates of first point
• (x₂,y₂) = coordinates of second point

Putting values,

Coordinate of mid point of diagonal AC:-

➺(3+x)/2 , (7+3)/2

➺(3+x)/2 , 10/2    

Coordinates of mid point of diagonal BD:-

➺(5+6 )/2 , (6+y) /2  

➺11/2 , (6+y)/2    

Comparing the x coordinates of mid point of both diagonals,

➺(3+x)/2=11/2

➺ 3+x=11

➺x=8

Comparing the y coordinates of midpoint of both diagonals,

➺(6+y)/2 = 10/2

➺6+y=10

➺y=4

Therefore,the values of x & y are 8,4 respectively.

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